26

Mobile Robotic Systems

26.1 Introduction
26.2 Fundamental Issues

Definition of a Mobile Robot • Stanford Cart •
Intelligent Vehicle for Lunar/Martian Robotic
Missions • Mobile Robots — Nonholonomic Systems

26.3 Dynamics of Mobile Robots
26.4 Control of Mobile Robots

26.1 Introduction

This subsection is devoted to modeling and control of mobile robotic systems. Because a mobile
robot can be used for exploration of unknown environments due to its partial or complete autonomy
is of fundamental importance. It can be equipped with one or more manipulators for performing
mission-specific operations. Thus, mobile robots are very attractive engineering systems, not only
because of many interesting theoretical aspects concerning intelligent behavior and autonomy, but
also because of applicability in many human activities. Attractiveness from the theoretical point of
view is evident because no firm fundamental theory covering intelligent control independent of
human assistance exists. Also, because wheeled or tracked mobile robots are nonholonomic mechan-
ical systems, they are attractive for nonlinear control and modeling research. In Section 26.2 of
this chapter, fundamental issues are explained regarding nonholonomic systems and how they differ
from holonomic ones. Although we will focus attention mostly on wheeled mobile robots, those
equipped with tracks and those that rely on legged locomotion systems are addressed as well. The


is an automatic, servo-controlled, freely programmable, multi-
purpose

manipulator

, with several axes, for the handling of workpieces, tools, or special devices.
Variably programmed operation make possible the execution of a multiplicity of tasks.
This definition clearly indicates that the term “industrial robot” is linked to a “manipulator,”
meaning that such a mechanical system is attached to a base. Typically, the base is fixed with
respect to a ground or single-degree-of-freedom platform mounted on rails. We also observe that
an industrial robot must have a programmable control system so that the same robot can be used
for different tasks.
A mobile robot has two essential features that are not covered by this definition. The first is
obviously mobility, and the second is autonomy. A minimum requirement for a mobile robot is to
be capable of traversing over flat horizontal surfaces. Given a point

A

on such a surface

S

, where
the robot is positioned at a time instant

t

, the mobile robot must be capable of reaching any other
point


z

-axis is normal to the surface (Figure 26.1). Clearly, the
position of any point on the surface is defined by coordinates (

x

,

y

). But, the position of the robot
is actually defined by the coordinates (

x

,

y,
φ

), where

φ
A

) to (

x

B

,

y

B

,
φ

B

) in a finite time interval

T

.
Mobility, as discussed above, is limited in terms of the system’s ability to traverse different
surfaces. The simplest case is a flat horizontal surface


y

, the ability of a wheeled robot to reach any desired point

B

from a
point

A

on the surface depends upon (1) the ability of the robot to produce enough driving force
to compensate for gravity force while moving toward the goal point; and (2) the presence of
sufficient friction forces between the wheels and the ground to prevent continuous slippage. Notice
also that there is no uniquely defined path between the points

A

and

B

, and the robot may be
incapable of traversing some trajectories, but still capable of reaching point

B

provided the trajectory
is conveniently selected.
In discussions related to mobility a fundamental question concerns climbing and descending

vehicle tilts backward while moving forward and finally reaches an inclination angle equal to that
of the staircase. The tread on the tracks engages with several stairs simultaneously, allowing the
robot to move forward.
In the second part of this section, the mobility will be highlighted from the standpoint of
nonholonomic constraints. We explain why a manipulator is a holonomic and why a mobile robot
is a nonholonomic system. Prior to that, though, we attempt to define a mobile robot. As mentioned
at the beginning of this section, the second essential feature of a mobile robot is autonomy. We
know that vehicles have been used as a means of transportation for centuries, but vehicles were
never referred to as “mobile robots” before, because the fundamental feature of a robot is to perform
a task without human assistance. In an industrial, well-structured environment it is not difficult to
program a robot manipulator to perform a task. On the other hand, the term “mobile robot” does
not necessarily correlate to an industrial environment, but a natural or urban environment. Industrial
mobile robots are called automatic guided vehicles (AGVs). AGVs are mobile platforms typically
guided by an electromagnetic source (a set of wires) placed permanently under the floor cover.
Tracking of the guidelines is realized through a simple feedback/feedforward control. Thus, an
AGV is not referred to as a mobile robot because it is not an autonomous system.
An autonomous system must be capable of performing a task without human assistance and
without relying on an electronic guidance system. It must have sensors to identify environmental
changes, and it must incorporate planning and navigation features to accomplish a task. More details
about these features are given in later sections, but now we provide an example of a simple mobile
robot currently used in urban environments: a vacuum-cleaning mobile robot. Such commercially
available robots have an ultrasonic-based range-finder mounted on a pan-and-tilt unit. This unit is
located on the front end of the chassis and constantly rotates left-and-right and up-and-down
independently of the speed of the vehicle. The range-finder is an ultrasonic transceiver/receiver
sensor mounted on the unit end-point. The echoes are processed by an on-board computer to identify
obstacles around the robot. A planner is a software module that describes the “desired path” so
that cleaning is performed uniformly all over the floor surface. The navigator is the software module
that provides changes in desired trajectories in accordance with the obstacles/walls located by the
sensorial system. Such a robot will automatically slow down and avoid a collision should another
vehicle or a human traverse its trajectory. Clearly, autonomy is not necessarily correlated to artificial

© 2002 by CRC Press LLC26.2.2 Stanford Cart

The cart was developed at the Stanford Artificial Intelligence Laboratory as a research setup for
Ph.D. students (Figure 26.2). The robot was equipped with an on-board TV system and a computer
dedicated to image processing and driving the vehicle through obstacle-cluttered spaces. The system
gained its knowledge entirely from images. Objects were located in three dimensions, and a model
of the environment was built with information gained while the vehicle was traversing a terrain.
The system was unreliable for long runs and very slow (1 m in 10 to 15 min).
The operation would start at a certain point on a flat horizontal surface (flat floor) cluttered with
obstacles. The camera was mounted on a sliding unit (50-cm track on top of the chassis) so that
it was able to move sideways while keeping the line-of-sight forward. Such sidewise movements
allowed the collection of several images of the same scene with a fixed lateral offset. By correlating
those images the control system was able to identify locations of obstacles in the camera’s field of
vision. Control was simplified because these images were collected while the cart was inactive.
After identifying the location of obstacles as simple fuzzy ellipsoids projected on the floor surface,
the vehicle itself was modeled as a fuzzy ellipsoid projected on the same surface.
Based on the environment model a Path Planner was used to determine the shortest possible path
to the goal-point. This program was capable of finding the path that was either a straight segment
between the end and initial points, or a set of tangential segments and arcs along the ellipses
(Figure 26.3). To simplify the algorithm, the ellipses were actually approximated by circles.
The navigation module was very primitive because the chart motor control lacked feedback.
Thus, the vehicle was moved roughly in a certain direction by activating, driving, and steering
motors for a brief time. After moving the vehicle for about 1 m, the whole procedure was repeated.
Although the whole process was extremely slow (roughly 4 to 6 m/h), and vehicle control very
primitive, this was one of the first platforms that had all features needed for a robot to be regarded
as a real mobile robot. It was autonomous and adaptable to environmental variations.

minerals). The base would allow building plants for the production of oxygen and hydrogen for
rocket fuel, helium for nuclear energy, and some metals. These materials would be used for building
space stations with a cost far lower than the cost of transporting them from Earth.
The IRVS consists of a mobile platform, a manipulator arm, and a set of mission sensors. The
most important requirement for the platform is exceptionally high payload-to-mass ratio. This was
achieved by using a Stewart platform system developed by the U.S. National Institute of Standards
and Technology (Figure 26.4). The structure consists of (1) an octahedral frame constructed of thin
walled aluminum tubing, (2) three wheel assemblies (two of them have speed/skid steering control,
while the third is a single free wheel), and (3) a work platform suspended by six cables arranged
as a Stewart platform. The system is equipped with two high-resolution cameras with power zoom,
auto iris, and focus capabilities mounted on a pan/tilt unit at the top of the octahedral frame.
Ultrasonic ranging sensors were added for detects objects within a range of 0.2 to 12 m with a
field of view of 6°. The system is also equipped with roll-and-pitch sensors that are used for
controlling the six cables so that the work platform is always horizontal.

FIGURE 26.3

Path Planning results for two distinct scenarios: (a) a straight line segment exists between the initial
and final point,

A

and

B

; and (b) a path consists of a set of straight segments tangential to augmented obstacles,
and arcs along the obstacle boundaries that are optimal in terms of its length.


(SCP)

selector

, (3) SCP

recorder

, and (4)
SCP

organizer

.
The site-navigator uses a potential field method to calculate the vehicle’s trajectory to the next
SCP based on vision and range measurements. The alternative SCP selector picks an alternative
SCP when a scheduled SCP cannot be reached due to obstacles/craters. The SCP recorder marks
the points already visited so that the vehicle cannot sample a SCP twice. The SCP organizer
generates a sequence of manipulator and instrument deployment tasks when the robot arrives at a
SCP.
The coordination level contains

task-dispatcher

and

behavior arbitrator

programs. The task-


degrees of freedom is described by
(26.1)
where

H

(

q

) is the

n
×
n

inertia matrix; is the

n

-vector due to gravity, centrifugal, and Coriolis
forces;



is the

m

vector of constraint forces. The constraint
equation generally has the form
(26.2)
Hqq hqq J q f
T
() (,) ()
.. .
+=−τ
hqq(, )
.
Cqq(,)
.
= 0

8596Ch26Frame Page 712 Friday, November 9, 2001 6:25 PM
© 2002 by CRC Press LLCwhere

C

is an

m


FIGURE 26.6

A manipulator in contact with the environment.
qq
qq
qq
32
42
5
2
0
0
0
+−=
−=
+−=
π
π
qq
qq
qqqq
14
23
1234
0
0
30
−=
−=


C; an angle
φ
between the longitudinal axis
of the chassis (x
b
) and the x-axis of the reference frame; and
θ
L
and
θ
R
, the angular displacements
of the left and right wheel, respectively. We assume that the wheels are independently driven and
parallel to each other. The distance between the wheels is l.
The constraint equations can be derived from the fact that the vehicle velocity vector v is always
along the axis x
b
. In other words, the lateral component of the velocity vector (the one that is normal
to the wheels) is zero. From Figure 26.7 we observe that the unit vector along x
b
is ,
while the vector normal to direction of motion is
Because , and v⋅n = 0, we obtain the first constraint equation:
(26.3)
The other two constraint equations are obtained from the condition that the wheels roll, but do not
slip, over the ground surface:
where v
R
(v

vr
R
R
L
L
=
=
θ
θ
.
.
θ
.
R
θ
.
L
vx y=+
..
cos sin
φφ
xv
.
cos=
φ
yv
.
sin=
φ
8596Ch26Frame Page 714 Friday, November 9, 2001 6:25 PM